Modeling air-to-water sound transmission using standard numerical codes of underwater acoustics

Abstract

In a recent paper [D. M. F. Chapman and P. D. Ward, J. Acoust. Soc. Am. 87, 601–618 (1990)], it was shown that a normal mode underwater acoustic propagation code can be modified to model air-to-water sound transmission simply by altering the mode excitation coefficients. These new coefficients are the exact wave-theoretic expressions for the air-to-water transmission problem. Herein, it is shown that if the height of the source above the surface is sufficiently small, then the air-to-water transmission problem can be approximated accurately by replacing the source in air with a source in water at a depth d ≪ λ below the surface, where λ is the acoustic wavelength in water. For a distant receiver in water, both the true source in air and the effective source in water exhibit nearly identical dipole radiation patterns. Although the effective directivity of the two sources is the same, the source strength is not. The correct transmission loss due to a source in air can be recovered from the transmission loss computed for a shallow source in water by adding the quantity 20 × log10 (ka d), where k s is the wave number in air. Using this approach, numerical results for three standard underwater acoustic models (normal mode, multipath expansion, parabolic equation) will be compared to benchmark results provided by the SAFARI model for a generic air-to-water transmission example.